Based on aberration theory,the design method of beam expander is detailed through an example.A beam expander is presented:the entrance pupil diameter of its objective is 200mm,focal length is 400mm,the field of view is 2mrad,the magnitude ratio is 40 and the primary working wavelength is 0.6328μm.The results of optical design have been given.When the distances between the objective and eyepiece are adjusted reasonably,the beam expander can be also used laser with wavelengths of 0.532μm or 1.064μm with the same magnitude ratio.It is no use to design new beam expander systems or eyepiece systems for these 3 waves.It can be used easily and save a lot of costs.